Right Bol Loop 16.11.2.222 of order 16


0123456789101112131415
1230574698111013121514
2301765411109814151213
3012647510118915141312
4576013212151314810119
5764120315121413108911
6457302113141215911108
7645231014131512119810
8911101413151201324576
9111081312141510236754
1089111514121332015467
1110891215131423107645
1215141311109845670123
1312151491181067451032
1413121589101176542301
1514131210811954763210

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   4   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

11 Elements of order 2:   2   4   7   8   9   10   11   12   13   14   15

4 Elements of order 4:   1   3   5   6

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (12,14)(13,15) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001